You probably should mention that restriction explicitly.
The article already considers in passing a board with two shapes of cells!
A Dabbaba-averse square board has two different cell shapes -- square for
the Dabbaba-binding a Ferz step from the removed one, pentagonal for the
other two.
The article covers at least five of the eleven Dual-Uniform tilings, which
are my above list restricted to use only one kind of cell. Of the other
six, at least the Rhombille and the Floret pentagonal tiling can be handled
as averse boards.